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Transactions of the American Mathematical Society

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Semigroup $ C^*$-algebras of $ ax+b$-semigroups


Author: Xin Li
Journal: Trans. Amer. Math. Soc. 368 (2016), 4417-4437
MSC (2010): Primary 46L05; Secondary 11R04, 13F05
DOI: https://doi.org/10.1090/tran/6469
Published electronically: September 15, 2015
MathSciNet review: 3453375
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Abstract: We study semigroup $ C^*$-algebras of $ ax+b$-semigroups over integral domains. The goal is to generalize several results about $ C^*$-algebras of $ ax+b$-semigroups over rings of algebraic integers. We prove results concerning K-theory and structural properties like the ideal structure or pure infiniteness. Our methods allow us to treat $ ax+b$-semigroups over a large class of integral domains containing all noetherian, integrally closed domains and coordinate rings of affine varieties over infinite fields.


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Additional Information

Xin Li
Affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
Email: xin.li@qmul.ac.uk

DOI: https://doi.org/10.1090/tran/6469
Received by editor(s): December 2, 2013
Received by editor(s) in revised form: April 29, 2014
Published electronically: September 15, 2015
Additional Notes: This research was supported by the ERC through AdG 267079
Article copyright: © Copyright 2015 American Mathematical Society

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